Create agents in 3D space

Author: Lukas Breitwieser
In this tutorial we want to demonstrate different functions to initialize agents in space.

Let's start by setting up BioDynaMo notebooks.

%jsroot on
gROOT->LoadMacro("${BDMSYS}/etc/rootlogon.C");

INFO: Created simulation object 'simulation' with UniqueName='simulation'.

We use SphericalAgents with $diameter = 10$ for all consecutive examples.

auto create_agent = [](const Double3& position) {
  auto* agent = new SphericalAgent(position);
  agent->SetDiameter(10);
  return agent;
};

We define the number of agents that should be created for functions that require this parameter.

uint64_t num_agents = 300;

We define two helper functions that reset the simulation to the empty state and one to visualize the result.

void Clear() {
  simulation.GetResourceManager()->ClearAgents();
}

void Vis() {
  simulation.GetScheduler()->FinalizeInitialization();
  VisualizeInNotebook();
}

Create agents randomly inside a 3D cube

Cube: $x_{min} = y_{min} = z_{min} = -200$ and $x_{max} = y_{max} = z_{max} = 200$
By default a uniform random number distribution is used.

Clear();
ModelInitializer::CreateAgentsRandom(-200, 200, num_agents, create_agent);
Vis();

Create agents randomly inside a 3D cube using a gaussian distribution

Cube: $x_{min} = y_{min} = z_{min} = -200$ and $x_{max} = y_{max} = z_{max} = 200$
Gaussian: $\mu = 0$, $\sigma = 20$
Note the extra parameter $rng$ passed to CreateAgentsRandom

Clear();
auto rng = simulation.GetRandom()->GetGausRng(0, 20);
ModelInitializer::CreateAgentsRandom(-200, 200, num_agents, create_agent, &rng);
Vis();

Create agents randomly inside a 3D cube using an exponential distribution

Cube: $x_{min} = y_{min} = z_{min} = -200$ and $x_{max} = y_{max} = z_{max} = 200$
Exponential: $\tau = 100$
Note the extra parameter $rng$ passed to CreateAgentsRandom

Clear();
auto rng = simulation.GetRandom()->GetExpRng(100);
ModelInitializer::CreateAgentsRandom(-200, 200, num_agents, create_agent, &rng);
Vis();

Create agents randomly inside a 3D cube using a 3D gaussian distribution

Cube: $x_{min} = y_{min} = z_{min} = -200$ and $x_{max} = y_{max} = z_{max} = 200$
3D gaussian: $\mu_x = \mu_y = \mu_z = 0$, $\sigma_x = 100$, $\sigma_y = 50$, $\sigma_z = 20$
The gaussian distribution we used earlier in this tutorial used the same parameters $\mu$ and $\sigma$ for all three dimentions. In this example we want to use different values for $\sigma$ in each dimension. Therefore we have to use a 3D guassian. Since BioDynaMo does not have a predefined 3D gaussian, we have to define the function ourselves.

Clear();
auto gaus3d = [](const double* x, const double* params) {
    auto mx = params[0];
    auto my = params[2];
    auto mz = params[4];
    auto sx = params[1];
    auto sy = params[3];
    auto sz = params[5];
    auto ret = (1.0/(sx * sy * sz *std::pow(2.0*Math::kPi, 3.0/2.0))) * 
        std::exp(-std::pow(x[0] - mx, 2.0)/std::pow(sx, 2.0) - 
                  std::pow(x[1] - my, 2.0)/std::pow(sy, 2.0) - 
                  std::pow(x[2] - mz, 2.0)/std::pow(sz, 2.0));
    return ret;
};
auto* random = simulation.GetRandom();
auto rng = random->GetUserDefinedDistRng3D(gaus3d, {0, 100, 0, 50, 0, 20}, 
                                           -200, 200, -200, 200, -200, 200);
ModelInitializer::CreateAgentsRandom(-200, 200, num_agents, create_agent, &rng);
Vis();

Create agents randomly on a sphere

Center of the sphere ${0, 0, 0}$
Radius: 100

Clear();
ModelInitializer::CreateAgentsOnSphereRndm({0, 0, 0}, 100, num_agents, 
                                           create_agent);
Vis();

Create 3D grid of agents

Number of agents per dimension: 10
Space between agents: 20
With this parameters Grid3D will create 1000 agents.

Clear();
uint64_t agents_per_dim = 10;
double space_between_agents = 20;
ModelInitializer::Grid3D(10, 20, create_agent);
Vis();

Create agents on a surface

We create agents between $x_{min} = y_{min} = -100$ and $x_{max} = y_{max} = 100$ with spacing of 10 beween agents. The $z$-coordinate is defined by the function $f(x, y) = 10 * sin(x/20) + 10 * sin(y/20)$

Clear();
auto f = [](const double* x, const double* params) {
    return 10 * std::sin(x[0] / 20.) + 10 * std::sin(x[1] / 20.0);
};
ModelInitializer::CreateAgentsOnSurface(f, {}, -100, 100, 10, -100, 100, 10, 
                                        create_agent);
Vis();

Create agents on a surface randomly

We use the same parameters as in the example before, but this time we want to place agents randomly on this surface. Therefore, $x$, and $y$ coordinate are sampled from a uniform distribution between $x_{min} = y_{min} = -100$ and $x_{max} = y_{max} = 100$.

Clear();
ModelInitializer::CreateAgentsOnSurfaceRndm(f, {}, -100, 100, -100, 100, num_agents, 
                                            create_agent);
Vis();